package algorithm.problems.array;

/**
 * Created by gouthamvidyapradhan on 10/03/2019
 * A group of two or more people wants to meet and minimize the total travel distance. You are given a 2D grid of
 * values 0 or 1, where each 1 marks the home of someone in the group. The distance is calculated using Manhattan
 * Distance, where distance(p1, p2) = |p2.x - p1.x| + |p2.y - p1.y|.
 * <p>
 * Example:
 * <p>
 * Input:
 * <p>
 * 1 - 0 - 0 - 0 - 1
 * |   |   |   |   |
 * 0 - 0 - 0 - 0 - 0
 * |   |   |   |   |
 * 0 - 0 - 1 - 0 - 0
 * <p>
 * Output: 6
 * <p>
 * Explanation: Given three people living at (0,0), (0,4), and (2,2):
 * The point (0,2) is an ideal meeting point, as the total travel distance
 * of 2+2+2=6 is minimal. So return 6.
 * <p>
 * Solution: O(N ^ 2 + M ^ 2) + O(N x M): Calculate the total number of persons in each row and each column and then
 * take a minimum of cartesian product of each row and each column.
 */
public class BestMeetingPoint {

    /**
     * Main method
     *
     * @param args
     */
    public static void main(String[] args) {
        int[][] grid = {{1, 0, 0, 0, 1}, {0, 0, 0, 0, 0}, {0, 0, 1, 0, 0}};
        System.out.println(new BestMeetingPoint().minTotalDistance(grid));
    }

    public int minTotalDistance(int[][] grid) {
        int[] countR = new int[grid.length];
        int[] countC = new int[grid[0].length];

        int[] distR = new int[grid.length];
        int[] distC = new int[grid[0].length];

        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid[0].length; j++) {
                if (grid[i][j] == 1) {
                    countR[i]++;
                    countC[j]++;
                }
            }
        }

        for (int i = 0; i < distR.length; i++) {
            for (int j = 0; j < distR.length; j++) {
                if (countR[j] != 0) {
                    distR[i] += Math.abs(j - i) * countR[j];
                }
            }
        }

        for (int i = 0; i < distC.length; i++) {
            for (int j = 0; j < distC.length; j++) {
                if (countC[j] != 0) {
                    distC[i] += Math.abs(j - i) * countC[j];
                }
            }
        }

        int min = Integer.MAX_VALUE;
        for (int i = 0; i < distR.length; i++) {
            for (int j = 0; j < distC.length; j++) {
                min = Math.min(min, distR[i] + distC[j]);
            }
        }

        return min;
    }
}
